Thursday, April 21, 2016

More Math - a Lathe Countershaft

So, I already found math is very useful for calculating new change gears.  One question that has been bothering me is.... how fast does the treadmill motor turn?  It's from a NordicTrack C2000, and the motor is a Quadra M-204432.  It simply says "2.60 Peak Watts" and "1.5 Continuous Watts".  No specs on RPM.  I finally decided to determine how fast the little thing was turning, so I ran out and grabbed a few measurements.

The treadmill had a max peak of 10 Miles/Hour.  That equates to 10x5280 Feet/Hour, or 52800 Feet/Hour.  For RPM, we need a Per Minute, so we have to divide that by 60 (because everyone knows there are sixty minutes in an hour).  That gives us a distance traveled of 880 feet per minute at 10 miles per hour.  My units of measurement are in inches, so I have to multiply that by 12.  My final Max speed is 10,560 inches per minute.

I grabbed the diameter of the bar that the tread was turned by (a rod that sits on two bearings).  It came out to 6 1/8", or 6.125".  To get the maximum speed, the outside has to travel around 1724.081633 times per minute.  Incidentally, 1725 RPM is a standard motor speed.  But, we're not even to the motor yet - we're still on the treadmills rolling pin speed.  Now, the pulley ratios come in to play.

Calculating a pulley ratio is fairly simple.  Divide the diameter of the driving (or motor) pulley by the corresponding pulley on the other side.  In my case, the motor pulley is 1.125" across, and the rolling pin pulley is 3.5" across, or a ratio of 0.285714286.  Now, one is normally converting from motor speed to spindle speed for things like lathes (which is "multiply the motor speed by the ratio"), but we are going backwards.  We have to divide the speed above, so the final ratio comes out to....

... 6,037.5 RPM?  That doesn't make much sense.

But, it IS close to 6,000 RPM, and there are definitely treadmill motors out there that turn that fast.  However, I do not really want the lathe turning at 6,000 RPM, so I need to reduce the speed.  This countershaft will do two things for me - it will help me reduce the speed of the spindle (the torque will go up at the spindle), and it will let me convert from a serpentine belt to a v-belt, which is what I have on the lathe.

1725 is a good "don't kill yourself speed", but if using things like 3 jaw chucks, I'd probably say closer to 1200 RPM is a max.  I need a pulley ratio of 0.25 or lower to feel comfortable, but with the controller for speed, 0.25 is about right.  That would give me a maximum of 1500 RPM at the spindle - if I can hit the pulley ratio.  The right pulley size without a countershaft would be a 4.5" pulley.  My lathe spindle pulleys are 5" - so close enough, as it would slow me down a bit more - but I have to convert from serpentine to v-belt.

My problem is that I could only find a serpentine belt pulley that would match my motor pulley that was 2.2" across.  So, if I get a v-belt pulley that is close to the 2.2" across, that would eliminate the countershaft as the speed changer, and we'd only have to calculate motor-to-spindle - but they don't make them.  They do make 2.5" v-belt pulleys.  So, since I thought it would be close enough, I bought them, the 2.2" serpentine pulley, some CRS round bar and square tubing, a couple of pillow block bearings, and welded it onto a frame that can be put onto a hinge and bolted to the lathe table.  Before you look closely at the picture - remember, my welding was never professional - sometimes I just stink at it.

Because I have different diameters on the countershaft, we HAVE to calculate the speed of the countershaft, and then the speed of the spindle from the countershaft.  We do the work twice.

So, a 1.125" pulley to a 2.2" pulley is a ratio of 0.511363636 .  A 2.5" pulley to a 5" pulley is a ratio of exactly 0.5.  That means our final ratio on the countershaft is 0.255681818.  That ratio takes 6,000 RPM down to .... 1,534.09090909.

And a maximum of 1,534 RPM at the spindle is perfectly acceptable.  It's only spinning at 25 times per second.

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